Unified M-estimation of matrix exponential spatial dynamic panel specification

This is the authors' abstract. We don't add key points for this paper.

In this paper, a unified M-estimation method in Yang (2018 Yang, Z. (2018). Unified M-estimation of fixed-effects spatial dynamic models with short panels. Journal of Econometrics 205(2):423–447. doi:https://doi.org/10.1016/j.jeconom.2017.08.019[Crossref], [Web of Science ®] , [Google Scholar]) is extended to the matrix exponential spatial dynamic panel specification (MESDPS) with fixed effects in short panels. Similar to the STLE model which includes the spatial lag effect, the space-time effect and the spatial error effect in Yang (2018 Yang, Z. (2018). Unified M-estimation of fixed-effects spatial dynamic models with short panels. Journal of Econometrics 205(2):423–447. doi:https://doi.org/10.1016/j.jeconom.2017.08.019[Crossref], [Web of Science ®] , [Google Scholar]), the quasi-maximum likelihood (QML) estimation for MESDPS also has the initial condition specification problem. The initial-condition free M-estimator in this paper solves this problem and is proved to be consistent and asymptotically normal. An outer product of martingale difference (OPMD) estimator for the variance-covariance (VC) matrix of the M-estimator is also derived and proved to be consistent. The finite sample property of the M-estimator is studied through an extensive Monte Carlo study. The method is applied to US outward FDI data to show its validity.